Innermost stable circular orbits of spinning test particles in Schwarzschild and Kerr space-times

Abstract

We consider the motion of classical spinning test particles in Schwarzschild and Kerr metrics and investigate innermost stable circular orbits (ISCO). The main goal of this work is to find analytically the small-spin corrections for the parameters of ISCO (radius, total angular momentum, energy, orbital angular frequency) of spinning test particles in the case of vectors of black hole spin, particle spin and orbital angular momentum being collinear to each other. We analytically derive the smallspin linear corrections for arbitrary Kerr parameter a. The cases of Schwarzschild, slowly rotating and extreme Kerr black hole are considered in details. For a slowly rotating black hole the ISCO parameters are obtained up to quadratic in a and particle's spin s terms. From the formulae obtained it is seen that the spin-orbital coupling has attractive character when spin and angular momentum are parallel and repulsive when they are antiparallel. For the case of the extreme Kerr black hole with co-rotating particle we succeed to find the exact analytical solution for the limiting ISCO parameters for arbitrary spin. It has been shown that the limiting values of ISCO radius and frequency do not depend on the particle's spin while values of energy and total angular momentum depend on it. We have also considered circular orbits of arbitrary radius and have found small-spin linear corrections for the total angular momentum and energy at given radius. System of equations for numerical calculation of ISCO parameters for arbitrary a and s is also explicitly written.

Innermost stable circular orbit of Kerr-MOG black hole

“…To find the circular orbit in any metric one considers the effective potential for the motion of a massive particle or photon [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. We approach the problem by solving ISCO by the well-developed method different from the one that Moffat has proposed [11,18,19].…”

“…The radius of the ISCO is 6M (M is the total mass of a black hole) in the case of the Schwarzschild black hole, while the radius of ISCO for a Kerr black hole depends on the intrinsic angular momentum a, the well-known Kerr parameter. As an example, the ISCO of the extreme rotating black hole, which has the intrinsic angular momentum of a Kerr black hole, which is M (a = M); we have M in the co-rotating and 9M in the counter-rotating cases where G N = c = 1 in the case of the Schwarzschild and Kerr metric [17]. ISCOs assist the study which finds the shape of thin disks and Penrose processes at the ergosphere as well as properties in the vicinity of the black hole.…”

Kerr-Sen black hole as accelerator for spinning particles

“…It has been proved in [11] and [12] [13] [14] that the movement of a spinning particle deviates from a geodesic due to the gravitational interaction. The orbits of spinning particles has been computed based on the Mathisson-Papapetrou-Dixon (MPD) equation [18] [19]. Recently, some modification to the MPD equation was given in [15] [16] [17].…”

Parameters of innermost stable circular orbits of spinning test particles: Numerical and analytical calculations

“…In paper of Jefremov, Tsupko & BisnovatyiKogan [1] we have analytically obtained the small spin corrections for the ISCO parameters for the Kerr metric at arbitrary value of Kerr parameter a. The cases of Schwarzschild, slowly rotating and extreme Kerr black hole were considered in details.…”

“…3. For the case of the extreme Kerr back- 1 In this paper we use the system of units where G = c = 1, the Schwarzschild radius R S = 2M , and other physical quantities which will be introduced further have the following dimensionalities: ground the difference between these two variants is quite considerable: we have 9M for the antiparallel and M for the parallel orientation. The parameters of ISCO in the Kerr space-time for a nonspinning particle were obtained in works of Ruffini & Wheeler [5] and Bardeen, Press & Teukolsky [6].…”